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Return sets of a linear control process

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Given a realn ×n matrixA and a nonempty set Γ of the Euclidean space ℝn, the linear control process

$$\dot x = Ax - c,c(t) \in \Gamma ,$$

defines several kinds of transferable (or reachable) sets. Among these, we study in detail return sets whose points are transferable into themselves after a certain period, and we consider the problem of minimizing such period.

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Dedicated to L. Cesari

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Conti, R. Return sets of a linear control process. J Optim Theory Appl 41, 37–53 (1983). https://doi.org/10.1007/BF00934435

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Key Words

  • Linear control processes
  • minimum period